Optimizes hyperparameter tuning for models using approximate leave-one-out cross-validation.
problem Finding optimal hyperparameters for regularized models using approximate leave-one-out cross-validation.
method Derive efficient formulas for gradient and hessian of approximate leave-one-out cross-validation, apply second-order optimization.
result Demonstrates the effectiveness of the approach on real-world data sets.
ALO-CV approximates leave-one-out error in proportional regime.
problem Estimating generalization error in high-dimensional settings.
method Developed new analysis for ALO-CV, showed consistency under strong convexity.
result ALO-CV approximates leave-one-out error up to negligible error.
Optimizes Lasso hyperparameters using leave-one-out CV.
problem Finding optimal hyperparameters for Lasso regression.
method Develops an algorithm to compute exact or approximate leave-one-out CV.
result Algorithm finds optimal hyperparameters for Lasso.
Paper accelerates conformal prediction by using approximate leave-one-out estimators.
problem Limited computational cost for conformal prediction.
method Incorporates approximate leave-one-out estimators to accelerate conformal prediction.
result ALO-based methods achieve comparable coverage and efficiency to exact methods but with significantly reduced runtime.
The paper improves ALO for ℓ1-regularized models.
problem Estimating out-of-sample error for ℓ1-regularized models. method Developed a novel theory for ℓ1-regularized problems, bounding ALO error. result For ℓ1-regularized problems, ALO error goes to zero as p goes to infinity. Improved LOO cross-validation for function approximation.
problem Estimating the Integrated Squared Error (ISE) for function approximation.
method Weighted Leave-One-Out cross-validation based on Gaussian Process.
result Significantly more precise ISE estimation compared to unweighted LOO.
Model inference, such as model comparison, model checking, and model selection, is an important part of model development. Leave-one-out cross-validation (LOO) is a general approach for assessing the generalizability of a model, but unfortunately, LOO does not scale well to large datasets. We propose a combination of u…
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…
Paper proposes diagnostics for error and variance estimation in randomized matrix computations.
problem Safe use of randomized matrix algorithms in applications.
method Leave-one-out error estimator and jackknife resampling method.
result Provides rapid diagnostics to assess quality of randomized matrix computations.
Proposes DeGLIF to denoise graph data for label noise robustness.
problem Label noise in graph data makes node classification challenging.
method Uses leave-one-out influence function to denoise graph data.
result DeGLIF improves accuracy in node classification on noisy datasets.
VarGrad reduces variance in ELBO gradient estimation for variational inference.
problem Improving the variance of gradient estimators in variational inference.
method VarGrad uses a new log-variance loss to estimate the ELBO gradient, achieving lower variance than the score function method.
result VarGrad offers a lower variance gradient estimator compared to other methods.
New method optimizes hyperparameters for non-smooth problems efficiently.
problem Efficiently tuning hyperparameters for non-smooth cost functions.
method Combines hyperparameter search with proximal gradient updates.
result Method converges to local optimum of LOO validation error.
Study shows influence functions are poor for neural networks but useful for identifying influential examples.
problem Influence functions misalign with leave-one-out retraining in neural networks.
method Decomposed the discrepancy into five terms and studied their contributions across different architectures and datasets.
result Influence functions are a good approximation to the proximal Bregman response function (PBRF), useful for identifying influential examples.
UDM reparameterization improves language model generation.
problem Mismatch between UDM training objective and denoising posterior.
method Leave-one-out denoising and absorbing state reformulation.
result Improved UDM generation through leave-one-out parameterization.
Efficient PI for neural networks without distributional assumptions.
problem No distributional assumptions for efficient predictive inference.
method Differential privacy and linear approximation for leave-one-out models.
result Rigorous coverage guarantees with reduced computation.
RandALO speeds up risk estimation for large datasets.
problem Estimating out-of-sample risk for large, high-dimensional models.
method RandALO: a randomized approximate leave-one-out estimator.
result RandALO is a computationally efficient risk estimator in high dimensions.
Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.
problem Robust matrix completion with sparse noise.
method Alternates between projected gradient step for low-rank and thresholding step for sparse noise.
result Achieves linear convergence for general thresholding functions.
The paper analyzes LOCV for high-dimensional risk estimation, proving error bounds.
problem Estimating out-of-sample prediction error in high-dimensional settings.
method Theoretical analysis of leave-one-out cross validation (LOCV) in penalized regression.
result Finite sample upper bounds on LOCV error, showing it converges to zero as n,p → ∞.
Consider the following class of learning schemes: β^:=argminβ∑j=1nℓ(xj⊤β;yj)+λR(β),(1) where xi∈Rp and yi∈R denote the ith feature and response variable …
Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical properties of such estimates have been extensively studied in the low-dimensional setting…
Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size grows. To resolve this difficulty in the case of Bayesian linear regression, we dev…
The present paper provides a new generic strategy leading to non-asymptotic theoretical guarantees on the Leave-one-Out procedure applied to a broad class of learning algorithms. This strategy relies on two main ingredients: the new notion of Lq stability, and the strong use of moment inequalities. Lq stability e…
Enhances polynomial chaos models with uncertainty intervals.
problem Uncertainty quantification in surrogate models.
method Jackknife-based conformal prediction integrated into polynomial chaos expansions.
result Produces accurate predictive intervals for low-accuracy models.
LOO-StabCP speeds up CP for multiple predictions.
problem Balancing computational efficiency and prediction accuracy in CP.
method Leave-One-Out Stable Conformal Prediction (LOO-StabCP) using algorithmic stability.
result LOO-StabCP is faster and more accurate than RO-StabCP.
The paper proves LOO CV is reliable under estimator stability.
problem Ensuring the reliability of leave-one-out cross validation.
method Using concentration inequalities based on logarithmic Sobolev inequality.
result LOO CV is a valid procedure under estimator stability.
Bayesian model averaging, model selection and its approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates og convergence than other methods such as AIC and leave-one-out cross-validation. On the other hand, these other methods can br inconsistent. We identify the "catch-up …
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in thei…
Consider the following class of learning schemes: \begin{equation} \label{eq:main-problem1} \hat{\boldsymbolβ} := \underset{\boldsymbolβ \in \mathcal{C}}{\arg\min} \;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbolβ; y_j) + λR(\boldsymbolβ), \qquad \qquad \qquad (1) \end{equation} where $\boldsymbol{x}_i \in \mathbb{…
A fast method for LOOCV in k-NN regression reduces computation time.
problem Efficient computation of LOOCV for k-NN regression.
method Identical LOOCV estimate to (k+1)-NN MSE on training data.
result LOOCV computation can be done with (k+1)-NN regression once.
Study improves understanding of non-differentiable penalties in high-dimensional settings.
problem Theoretical understanding of non-differentiable penalties like generalized LASSO and nuclear norm in high-dimensional settings.
method Proportional high-dimensional regime analysis with finite sample upper bounds on expected squared error.
result LO provides accurate estimation of out-of-sample risk in high-dimensional settings.
Algorithm identifies and corrects noisy labels using Gaussian process regression.
problem Detecting and correcting real-valued noisy labels from mixed data.
method Gaussian process regression with heteroscedastic noise model and leave-one-out cross-validation.
result The method can pinpoint corrupted sample points and improve regression models.
New methods improve anomaly detection with reduced false positives.
problem Effective anomaly detection with controlled error rates.
method Leave-one-out-, bootstrap-, and cross-conformal anomaly detection methods.
result Improved anomaly detection with reduced false positives.
Backward Conformal Prediction offers flexible control over prediction set sizes while ensuring coverage guarantees.
problem Providing reliable prediction sets with controlled sizes in applications like medical diagnosis.
method Defines a rule that constrains prediction set sizes based on observed data, adapting coverage levels.
result Maintains computable coverage guarantees while ensuring interpretable, well-controlled prediction set sizes.
The least squares Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz (2001) is widely used for pricing Bermudan options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of avoiding it requires additional simulation paths. We present the leave-one-out LSM (LOOLSM) algor…
A new method improves robustness and efficiency of Bayesian LOO-CV.
problem Computational expense and unreliability of classical LOO-CV in high-dimensional Bayesian models.
method Proposes a mixture estimator to compute Bayesian LOO-CV criteria with finite asymptotic variance.
result Improved robustness and efficiency in high-dimensional problems.
Spectral methods achieve near-optimal performance in orthogonal and permutation group synchronization.
problem Recovering group elements from pairwise measurements in computer vision.
method Spectral methods applied with the leave-one-out technique.
result Near-optimal performance bounds for orthogonal and permutation group synchronization established.
We show how to adjust the coefficient of determination (R2) when used for measuring predictive accuracy via leave-one-out cross-validation.
The study evaluates different parameter selection methods for Gaussian process interpolation.
problem Choosing optimal parameters for Gaussian process interpolation.
method Empirical study using scoring rules and leave-one-out selection criteria.
result The choice of model family is often more important than the selection criterion.
Leave-one-out cross-validation (LOOCV) can be particularly accurate among cross-validation (CV) variants for machine learning assessment tasks -- e.g., assessing methods' error or variability. But it is expensive to re-fit a model N times for a dataset of size N. Previous work has shown that approximations to LOOCV…
Weighted SVM (or fuzzy SVM) is the most widely used SVM variant owning its effectiveness to the use of instance weights. Proper selection of the instance weights can lead to increased generalization performance. In this work, we extend the span error bound theory to weighted SVM and we introduce effective hyperparamete…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training po…
Many learning tasks, such as cross-validation, parameter search, or leave-one-out analysis, involve multiple instances of similar problems, each instance sharing a large part of learning data with the others. We introduce a robust framework for solving multiple square-root LASSO problems, based on a sketch of the learn…
LOO prediction method improves generalization guarantees for arbitrary datasets.
problem Understanding LOO error guarantees in fully transductive settings for arbitrary datasets.
method Median of Level-Set Aggregation (MLSA) for empirical-risk level sets.
result Multiplicative oracle inequality for LOO error with complexity scaling.
Cross validation (CV) and the bootstrap are ubiquitous model-agnostic tools for assessing the error or variability of machine learning and statistical estimators. However, these methods require repeatedly re-fitting the model with different weighted versions of the original dataset, which can be prohibitively time-cons…
Efficiently estimates shrinkage coefficient for RTME using LOOCV approximation.
problem Estimating optimal shrinkage coefficient for Regularized Tyler's M-estimator.
method Proposes an approximate LOOCV method to estimate α efficiently. result Significant speedup and accuracy improvement over existing methods.
A new KDE model prevents singular solutions and accelerates optimization for probabilistic modeling.
problem Adapting to varying densities in data regions for probabilistic modeling.
method Adaptive KDE model with individual bandwidths, LOO-MLL criterion, and modified EM algorithm.
result The proposed models prevent singular solutions and have promising performance.
Paper breaks down risk contribution into inherent and correlation risk components.
problem Understanding the sources of risk in portfolio contributions.
method Leave-one-out decomposition approach to separate inherent and correlation risk contributions.
result The decomposition reveals distinct contributions of position volatility and correlation to portfolio risk.
Quantifying the importance of each training point to a learning task is a fundamental problem in machine learning and the estimated importance scores have been leveraged to guide a range of data workflows such as data summarization and domain adaption. One simple idea is to use the leave-one-out error of each training …